If cos x + cos²x = 1, the numerical value of (sin12x

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If cos x + cos²x = 1, the numerical value of (sin¹²x + 3 sin¹⁰x + 3 sin⁸x + sin⁶x – l) is :

1. - 1
2. 2
3. 0
4. 1

Correct Option: C

cos x + cos² x = 1
⇒ cos x = 1 – cos² x = sin² x ...(i)
∴ sin¹²x + 3 sin¹⁰x + 3 sin⁸x + sin⁶x – 1
= (sin⁴ x + sin² x)³ – 1
= (cos²x + sin²x)³ – 1 [By (i)]
= 1 – 1 = 0